In 30 litres mixture of acid, the ratio of acid and water is 2:3. What amount of water should be added to the mixture so that the ratio of acid and water becomes 2:5?

Options

A. 10litres
B. 15litres
C. 18litres
D. 12litres

Answer

To solve the problem step by step, we need to determine how much water should be added to a 30-liter mixture of acid and water, where the initial ratio of acid to water is 2:3, so that the new ratio becomes 2:5.

### Step 1: Determine the initial amounts of acid and water in the mixture.
The total volume of the mixture is 30 liters, and the ratio of acid to water is 2:3.

- Total parts = 2 (acid) + 3 (water) = 5 parts
- Volume of 1 part = Total volume / Total parts = 30 liters / 5 = 6 liters

Now, calculate the amounts of acid and water:
- Amount of acid = 2 parts = 2 * 6 = 12 liters
- Amount of water = 3 parts = 3 * 6 = 18 liters

### Step 2: Set up the new ratio after adding water.
We want the new ratio of acid to water to be 2:5. Let’s denote the amount of water to be added as \( x \) liters.

After adding \( x \) liters of water, the new amount of water will be:
- New amount of water = 18 liters + \( x \) liters

The amount of acid remains the same at 12 liters.

### Step 3: Set up the equation based on the new ratio.
According to the new ratio:
\[ \frac{\text{Acid}}{\text{Water}} = \frac{2}{5} \]
Substituting the known values:
\[ \frac{12}{18 + x} = \frac{2}{5} \]

### Step 4: Cross-multiply to solve for \( x \).
Cross-multiplying gives:
\[ 12 * 5 = 2 * (18 + x) \]
\[ 60 = 36 + 2x \]

### Step 5: Isolate \( x \).
Subtract 36 from both sides:
\[ 60 - 36 = 2x \]
\[ 24 = 2x \]
Now divide by 2:
\[ x = 12 \]

### Conclusion:
The amount of water that should be added to the mixture is **12 liters**.

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